Dimension Reduction for High-dimensional Heteroskedastic VAR Models

Music City Center 

Many time series often exhibit heteroskedasticity, posing challenges for analysis. While multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) models offer solutions, they often suffer from overcapitalization, escalating parameter counts with dimensionality. In this presentation, we introduce a parsimonious approach to the vector autoregressive (VAR) model incorporating a heteroskedastic structure within the error terms. Our method provides substantial efficiency gains in model estimation by significantly reducing the number of parameters in the coefficient and conditional covariance matrices of VAR-MGARCH models. By parameterizing our method, redundant information within time series signals is eliminated, significantly reducing model complexity. We investigate the asymptotic properties of estimators and evaluate our approach through simulation studies and real-data analysis, offering enhanced modeling accuracy and computational efficiency for volatile financial time series.

Heteroskedasticity, Multivariate GARCH (MGARCH), Parsimonious Modeling.